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The density for a normal distribution converges to 0 in the limit to both positive and negative infinity. So it is not true that $ln(pdf(\theta_1)) > ln(pdf(\theta_0))$$\ln(\textrm{pdf}(\theta_1)) > \ln(\textrm{pdf}(\theta_0))$ for all $\theta_1$ and $\theta_0$. The reason that the density is larger for this normal distribution near its mean compared to the uniform distribution is because the variance of the normal distribution is small.

The density for a normal distribution converges to 0 in the limit to both positive and negative infinity. So it is not true that $ln(pdf(\theta_1)) > ln(pdf(\theta_0))$ for all $\theta_1$ and $\theta_0$. The reason that the density is larger for this normal distribution near its mean compared to the uniform distribution is because the variance of the normal distribution is small.

The density for a normal distribution converges to 0 in the limit to both positive and negative infinity. So it is not true that $\ln(\textrm{pdf}(\theta_1)) > \ln(\textrm{pdf}(\theta_0))$ for all $\theta_1$ and $\theta_0$. The reason that the density is larger for this normal distribution near its mean compared to the uniform distribution is because the variance of the normal distribution is small.

2 added 1 character in body
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The density for a normal distribution converges to 0 in the limit to both positive and negative infinity. So it is not true that $ln(pdf(\theta_1)) > ln(pdf(\theta_0))$ for all $\theta_1$ and $\theta_0$\theta_0$. The reason that the density is larger for this normal distribution near its mean compared to the uniform distribution is because the variance of the normal distribution is small.

The density for a normal distribution converges to 0 in the limit to both positive and negative infinity. So it is not true that $ln(pdf(\theta_1)) > ln(pdf(\theta_0))$ for all $\theta_1$ and $\theta_0. The reason that the density is larger for this normal distribution near its mean compared to the uniform distribution is because the variance of the normal distribution is small.

The density for a normal distribution converges to 0 in the limit to both positive and negative infinity. So it is not true that $ln(pdf(\theta_1)) > ln(pdf(\theta_0))$ for all $\theta_1$ and $\theta_0$. The reason that the density is larger for this normal distribution near its mean compared to the uniform distribution is because the variance of the normal distribution is small.

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The density for a normal distribution converges to 0 in the limit to both positive and negative infinity. So it is not true that $ln(pdf(\theta_1)) > ln(pdf(\theta_0))$ for all $\theta_1$ and $\theta_0. The reason that the density is larger for this normal distribution near its mean compared to the uniform distribution is because the variance of the normal distribution is small.